Howard made cards for the fractions 3/9,4/8, 1/7, 6/5,and 3/10. He set them out in a row, putting 1/7 first.The fraction equivalent to 1/2 went after the one equivalent to a mixed number. A fraction that is half of 3/5 went between the fraction equivalent to a mixed number and the one equivalent to 1/3. Fing the order of the cards.
i don't know that's what i need help with
To find the order of the cards, we need to follow the given clues and figure out the correct order step by step. Let's break down the given information:
1. Howard set the cards out in a row, putting 1/7 first.
This tells us that 1/7 is the first card.
2. The fraction equivalent to 1/2 went after the one equivalent to a mixed number.
This means that the card equivalent to a mixed number should come before the card equivalent to 1/2. Let's see which fractions can be equivalent to mixed numbers:
- 3/9 can be simplified to 1/3, which is not a mixed number.
- 4/8 can be simplified to 1/2, which is the equivalent of a mixed number (1 and 1/2).
- 1/7 is already in its simplest form and not a mixed number.
- 6/5 cannot be simplified to a proper fraction or a mixed number.
- 3/10 cannot be simplified either.
From this information, we can determine that the card equivalent to 1/2 is second.
3. A fraction that is half of 3/5 went between the fraction equivalent to a mixed number and the one equivalent to 1/3.
This clue helps us place the card equivalent to 3/5. Since it should be between the card that is equivalent to a mixed number (1/2) and the one equivalent to 1/3, we can deduce that the order should be: 1/7, 1/2, 3/5.
4. Now we have three cards left: 3/9, 6/5, and 3/10.
Let's simplify these fractions to find their equivalent forms:
- 3/9 simplifies to 1/3, which means it is equivalent to a mixed number.
- 6/5 cannot be simplified any further.
- 3/10 cannot be simplified either.
The remaining two cards, 6/5 and 3/10, need to be placed in the correct order. Since we already have a card equivalent to a mixed number (1/7) and one equivalent to 1/3 in their respective correct positions, we can determine that the order of the remaining fractions is: 1/7, 1/2, 3/5, 1/3, 3/9, 6/5, 3/10.
Therefore, the order of the cards is: 1/7, 1/2, 3/5, 1/3, 3/9, 6/5, 3/10.